Creating a Culture of Thinking

August 2, 2012

This September I'm planning to create a "Culture of Thinking" that I learned about from Peter Liljedahl at one of Alberta's High School Math Institutes--Professional Development implemented by the Alberta Regional Consortia in support of Alberta's new math program of studies.

I've decided to blog about this adventure so that other teachers might benefit from my learning experience in implementing an approach very different from "traditional" math classrooms. It should be interesting, since I've never done this before 😃 (blogged or used Peter's approaches).

For the benefit of teachers not familiar with Peter's ideas, and to help immerse myself in them, I've created a summary of my understandings gained from watching a number of videos of High School Math Institutes. Of course I can't summarize all of his ideas, and I won't understand them perfectly. These are the main ideas I will be concentrating on:

Not only do Peter's ideas resonate with me (I've come to many of the same conclusions re: how we actually discourage thinking), but one thing he said jumped out: If you are successful in creating a culture of thinking in your classroom, "teaching will be a joy". Who can argue with that?

Students Don't Think

We (educators) have created the system that encourages non-thinking. Here are some of the ways that we inadvertently create this environment:

The way we ask questions. For example, asking questions where only one student responds, thus others don't need to think, such as "What's the answer?" vs. "Tell me when you have an answer."

The way we answer questions. The vast majority of student questions are "stop thinking" questions. For example, "is this the right answer?"

The way we give notes. Traditional Notes are usually a copy of what's in the text. Taking notes replaces learning now with the drive to ensure they have material to maybe learn later. Not only that, but students rarely look at their notes. When preparing for a test, students use practice tests and review booklets (that we give them).

The way we "level". Leveling is the process of bringing all students up to the same level of understanding. We typically level to the highest level of skill or concept. This creates an assumption that you can't go on unless everyone is "level". It also demotivates students because students know they'll get the correct answer in 2 to 4 minutes, and that it'll be the best answer.

Create a Culture of Thinking (and Collaboration)

It is possible to create a classroom environment where students actually think and collaborate. Notice that I've slipped in "and Collaborate". Collaboration is crucial, as you'll see in the next section on using a Culture of Thinking.

There are three key ways to create this environment, as described below:

Change How Students Work Have students work
  • in random groups of 3 or 4 (randomized daily using a visible process)
  • standing
  • using non-permanent vertical surfaces

Paraphrased below are the reasons Peter lists for this very specific work environment.

  • Knowledge in a group is greater than that of the individuals
  • Less leveling is required (see the section Use Your Culture of Thinking below)
Random Groups with Visual Selection Process
  • Need to break down social barriers
  • Process must be visibly random so students don't think teacher has ulterior motives
Standing, Working on Vertical Surfaces
  • Students can't fake thinking. They can't hide any more
  • Teacher can see at a glance what each group is doing
  • Mobilization of knowledge: Students can see other work and ideas
Non-Permanent Surfaces
  • Students are more likely to take risks
  • Note: Windows are even better ("Cool! I'm solving problems like they do on CSI!")
Start from Day 1

Stop answering "stop thinking" questions, like "Is this the right answer?" Instead, direct them to other students or groups.

Give students one interesting, non-curricular task per day for the first six days. Consider using tasks from this doc on Peter's website. You may also want to look through Peter's links to other websites.

Believe in this process, because students will rise (or fall) to the expectations you have, whether explicit or implicit.

Note: According to Peter, it takes about three weeks for students to fully accept the teacher not answering "stop thinking" questions. Then they become confident and "develop certainty for themselves." Students stop asking how to do it, and start telling how to do it.

Use Your Culture of Thinking (and Collaboration)

When you have a Culture of Thinking, use it!

Use Upside-Down Lessons

Take what you want to achieve at the end of the lesson (typically found at the end of the lesson in a traditional textbook) and make that the opening problem. The "lesson" becomes formalizing the work (struggle) of the students during the period. This works every single time when you already have a culture of thinking.

I don't have a good example to point to on Peter's website, but I will write about what I choose in my classroom in the future. Wish me luck :-).

That said, one big idea I took from Peter's talks is to make the Mathematical Processes (as discussed in the Alberta program of studies front-matter) the content of your teaching, and the Specific Outcomes (also from the program of studies) the context of your teaching.

For quick reference, here are the mathematical processes from the Alberta program of studies:

  • Communication
  • [make] Connections
  • Mental Estimation and Mathematics
  • Problem Solving
  • Reasoning
  • [use of] Technology
  • Visualization
Leverage Your Collaborative Environment

Stop leveling, or level to the "bottom" (i.e. the level that every student achieved during the period). The idea that you can't go on without leveling to the highest level is only true when students are working individually. This is not true when they're collaborating in groups, and between groups.

Stop giving traditional notes. Consider the following options:

  • post online
  • give after the lesson
  • point to the text
  • point to work that the students did

Start giving meaningful notes:

  • what was interesting
  • what can't be found elsewhere (e.g. textbook, other student work)
  • what had meaning

Do a "gallery walk" around the room to highlight the things that are good or incomplete. Then send them back to their desks to write their own exemplar based on what they saw. This "glossary" (1 or 2 items per class) becomes the students' set of notes.

Use it or Lose It!

Peter mentioned a number of times that even when you have a well-tuned culture of thinking, it can be lost if you:

  • Try to teach (traditionally) too much
  • Give students questions directly from a traditional textbook

This is my understanding of Creating a Culture of Thinking (and Collaboration) at this point. Join me in September as I implement these ideas, and see what happens! The first day of classes is Tuesday, September 4, 2012.